On singularities of submanifolds of higher dimensional Euclidean spaces

Summary Generalizations of principle axes are found for surfaces in E⁴. The singularities generalize umbilics. The generic indicies are computed. For these computations the Thom Transversality Theorem as applied by Feldman to geometry is used. Hower we ? reduce the group ? rendering the calculations more tractible. Also we show that a torus or sphere cannot be immersed in E⁴ with everywhere nonzero curvature of the normal bundle. Entrata in Redazione il 19 novembre 1968.     

Synthesis of the aziridinomitosene skeleton by intramolecular Michael addition: alpha-lithioaziridines and nonaromatic substrates

The bicyclic pyrrole ketone 16 has been prepared by using an oxaza-Claisen rearrangement, followed by nitrogen deprotection. Coupling with the stannylaziridine mesylate 15a or nosylate 15b affords 17. Conversion to 40 provides a substrate for generation of an alpha-lithioaziridine 41 by tin lithium exchange. An intramolecular Michael addition pathway for 41 has been demonstrated by the isolation of 46 in 20% yield under conditions where the intermediate enolate 43 is trapped by selenenylation, but competing proton transfer gives 42. The synthetic potential of the process is limited by stability problems at the stage of the enolate 43 or the protonated product 44.     

Liquid chromatography/electrospray tandem mass spectrometric analysis of incurred ractopamine residues in livestock tissues

Ractopamine HCl is a beta-adrenergic agonist (beta-agonist) recently approved by the U.S. Food and Drug Administration, but not other governmental agencies, for use in finishing swine. For these reasons, it was important to develop and validate mass spectrometric methods for the detection and confirmation of ractopamine residues in livestock marker tissues. Incurred tissues in cattle, sheep, turkeys, and ducks were generated during 7-day ractopamine feeding (20 ppm in diets) periods. Disposition of ractopamine residues in liver and pigmented retinal epithelium was determined in animals slaughtered with withdrawal periods of 0, 3, and 7 days. Ractopamine residues, purified using solid-phase extraction, were measured using liquid chromatography (LC) and electrospray with detection by tandem mass spectrometry (MS/MS) in the multiple reaction-monitoring (MRM) mode. Total ractopamine residues (parent ractopamine + hydrolyzed conjugates) in liver were detected in all species on withdrawal day 0 (2-97 ppb) and were greatly diminished in all species by withdrawal day 7 (<1 ppb). Bovine and ovine retina had lower levels of ractopamine (0.5-3 ppb) than liver, and occular residues increased with withdrawal time, suggesting redistribution into this tissue. Lower limits of quantification were found to be approximately 0.1 ppb in liver and retina. Incurred ractopamine residues were confirmed by the precise and accurate agreement of MRM intensity ratios of diagnostic fragment ions (m/z 284, 164, and 121) from the protonated molecule between ractopamine residues in incurred samples and an authentic ractopamine standard. The limits of confirmation in liver and retina using recognized acceptance criteria were below 1 ppb. The high sensitivity and specificity for measurement and confirmation of ractopamine residues suggests this method will be applicable for regulatory residue surveillance programs.     

Sharp bounds for the number of 3‐independent partitions and the chromaticity of bipartite graphs

Given a graph G and an integer k ≥ 1, let α(G, k) denote the number of k‐independent partitions of G. Let ??^?s(p,q) (resp., ??₂^?s(p,q)) denote the family of connected (resp., 2‐connected) graphs which are obtained from the complete bipartite graph K_p,q by deleting a set of s edges, where p ≥ q ≥ 2. This paper first gives a sharp upper bound for α(G,3), where G ∈ ?? ^?s(p,q) and 0 ≤ s ≤ (p ? 1)(q ? 1) (resp., G ∈ ?? ₂^?s(p,q) and 0 ≤ s ≤ p + q ? 4). These bounds are then used to show that if G ∈ ?? ^?s(p,q) (resp., G ∈ ?? ₂^?s (p,q)), then the chromatic equivalence class of G is a subset of the union of the sets ??^?s_i(p+i,q?i) where max and s_i = s ? i(p?q+i) (resp., a subset of ??₂^?s(p,q), where either 0 ≤ s ≤ q ? 1, or s ≤ 2q ? 3 and p ≥ q + 4). By applying these results, we show finally that any 2‐connected graph obtained from K_p,q by deleting a set of edges that forms a matching of size at most q ? 1 or that induces a star is chromatically unique. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 48–77, 2001     

Sample indexed spatial orthogonal frequency division multiplexing

Optical spatial modulation(OSM) is a multiple-transmitter technique that can provide higher data rates with low system complexity as compared with single-input single-output systems. Orthogonal frequency division multiplexing(OFDM) is widely implemented to achieve better spectral efficiency in wireless channels. Asymmetrically clipped optical OFDM(O-OFDM) and DC-biased O-OFDM are two well-known O-OFDM techniques suitable for intensity-modulation direct-detection optical systems. In this work, sample indexed spatial OFDM(SIS-OFDM) is proposed to combine OSM and O-OFDM in a novel way and achieve significant performance gain. By assigning time-domain samples of the O-OFDM transmit symbol to different transmitters, SIS-OFDM achieves much better spectral efficiency and reduces computational complexity at the transmitter as compared with previous work that combines OSM with O-OFDM in the frequency domain. We also consider the impact of optical source biasing on overall performance, and the relative performance of imaging receiver(ImR) versus non-imaging receiver(NImR) design for our proposed SIS-OFDM technique. Results indicate that for an Ntx × Nrx multiple-input multiple-output configuration where Ntx = Nrx = 4, SIS-OFDM using ImR can achieve up to 135 dB of signal-to-noise ratio gain over comparable system using a NImR. Also, using Nsc number of O-OFDM subcarriers provides up to Nsc × log2(Ntx) additional bits per symbol of spectral efficiency over techniques that combine OSM and O-OFDM in the frequency domain.     

Infrared negative luminescent devices and higher operating temperature detectors

Infrared LEDs and negative luminescent devices, where less light is emitted than in equilibrium, have been attracting an increasing amount of interest recently. They have a variety of applications, including as a ‘source’ of IR radiation for gas sensing; radiation shielding for, and non-uniformity correction of, high sensitivity staring infrared detectors; and dynamic infrared scene projection. Similarly, infrared (IR) detectors are used in arrays for thermal imaging and, discretely, in applications such as gas sensing. Multi-layer heterostructure epitaxy enables the growth of both types of device using designs in which the electronic processes can be precisely controlled and techniques such as carrier exclusion and extraction can be implemented. This enables detectors to be made which offer good performance at higher than normal operating temperatures, and efficient negative luminescent devices to be made which simulate a range of effective temperatures whilst operating uncooled. In both cases, however, additional performance benefits can be achieved by integrating optical concentrators around the diodes to reduce the volume of semiconductor material, and so minimise the thermally activated generation-recombination processes which compete with radiative mechanisms. The integrated concentrators are in the form of Winston cones, which can be formed using an iterative dry etch process involving methane/hydrogen and oxygen. We present results on negative luminescence in the mid- and long-IR wavebands, from devices made from indium antimonide and mercury cadmium telluride, where the aim is sizes greater than 1 cm×1 cm. We also discuss progress on, and the potential for, operating temperature and/or sensitivity improvement of detectors, where very high-performance imaging is anticipated from systems which require no mechanical cooling.     

Accurate base composition of double-strand DNA by mass spectrometry

An accurate molecular weight (M_r) assignment for a double-strand (ds) DNA determines or greatly restricts the possible number of each of its four bases, while the compositions for its two single-strand (ss) components can also be derived from their M_r values. For a ds 64-mer (39 kDa), the ss-M_r values (± 0.5 Da) of its high-resolution mass spectrum from an electrospray ionization/Fourier transform instrument yield only the correct ds- and ss-base compositions. Literature mass spectra of lower mass accuracy show that such data can also restrict their possible composition assignments, with further discrimination using the abundance vs. base composition of small fragment ions from the dissociation of the ss molecular ions.     

Partition of a directed bipartite graph into two directed cycles

Let D = (V₁, V₂; A) be a directed bipartite graph with |V₁| = |V₂| = n 2. Suppose that d_D(x) + d_D(y) 3n + 1 for all x ε V₁ and y ε V₂. Then D contains two vertex-disjoint directed cycles of lengths 2n₁ and 2n₂, respectively, for any positive integer partition n = n₁ + n₂. Moreover, the condition is sharp for even n and nearly sharp for odd n.     

Practical analysis of high purity chemicals--V. Precision silver chloride gravimetry

A reasonably simple gravimetric silver chloride procedure with fairly wide tolerance in conditions is presented in full detail with all critical steps and precautions delineated. The procedure allows the precision determination of chloride by analysts having limited expertise with exacting gravimetric methods, and can be performed with equipment common to nearly all laboratories and without dependence on a standard substance. The elapsed and actual working times for the assessment of a solid sample in triplicate are 65 and 10-12 hr respectively. The application of the procedure to the assay of some high-purity chloride salts and to the standardization of hydrochloric acid solutions is described.